The twin paradox is an apparent contradiction in special relativity where each of two twins in relative motion expects the other to age more slowly, yet the travelling twin ages less because their paths through spacetime are not equivalent.
Consider twin Jane and Jill. Suppose Jane makes a round trip from Earth to a star system 10 light-years away and back at 80% the speed of light (). From Jill’s perspective on Earth, Jane takes
years to complete the entire trip. Using the time dilation equation
, where
, Jill calculates how much proper time elapses along Jane’s worldline and concludes that Jane ages
years during those 25 Earth years.
From Jane’s point of view, she is stationary and Jill is moving. A direct application of time dilation might suggest the opposite result, that Jill ages less, leading to an apparent paradox. However, due to length contraction, the distance to the star is no longer 10 light-years in Jane’s frame; it is reduced to light-years, with the round trip taking
years to complete.
Therefore, the two perspectives do not contradict each other: both agree that Jane ages less and experiences about 15 years during the journey. Although each twin sees the other’s clock running slow locally, Jane covers a shorter contracted distance at high speed. Applying time dilation and length contraction consistently shows that she ages less.
Question
Wouldn’t Jane’s spaceship need to accelerate (speed up, slow down or stop) when leaving Earth and at the turnaround point?
Answer
Not necessarily. The scenario can be reformulated so that no single traveller undergoes acceleration. Instead of departing from rest on Earth, Jane can be imagined as already moving at a constant speed and passing Earth. As she passes, she synchronises her clock with Jill’s. At the distant point 10 light-years away, a second spaceship carrying a third observer (Judy) passes Jane while moving towards Earth at the same constant speed. At that event, Judy compares clocks with Jane and then continues towards Earth. When Judy reaches Earth, her clock is compared with Jill’s. In this way, the entire analysis can be carried out using only inertial observers. The result is that the travelling clocks (Jane’s and Judy’s) accumulate less proper time than Jill’s clock on Earth.